Find the 74th percentile, P74, from the following data 13 14.3 14.4 17.5 18.6 19.1 20.3 20.7 21.9 22.6 26.7 27.9 28.1 28.8 30 32.1 35.8 36.7 37.8 38.3 39.2 39.9 41.2 42.5 47.7 49.6 49.8 P74 %3D
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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**Question 7**
Find the 74th percentile, \( P_{74} \), from the following data:
| | | | | | |
|---|---|---|---|---|---|
| 13.0 | 14.3 | 14.4 | 17.5 | 18.6 | 19.1 |
| 20.3 | 20.7 | 21.9 | 22.6 | 26.7 | 27.9 |
| 28.1 | 28.8 | 30.0 | 32.1 | 35.8 | 36.7 |
| 37.8 | 38.3 | 39.2 | 39.9 | 41.2 | 42.5 |
| 47.5 | 49.6 | 49.8 | | | |
\( P_{74} = \) [Input box]
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**Explanation:**
This exercise asks learners to determine the 74th percentile from a given dataset. The data are organized in a table format with multiple rows and columns. The values range from 13.0 to 49.8 and are presumably in ascending order.
To find the 74th percentile, one should follow these steps:
1. **Count the numbers**: Determine the total number of data points.
2. **Calculate the rank**: Use the formula \((P/100) \times (N+1)\) where \(P\) is the percentile (74 in this case) and \(N\) is the total number of data points.
3. **Locate the percentile**: Use the calculated rank to find the value in the dataset.
This exercise aids in understanding how to calculate and interpret percentiles, which are essential for statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef4421a9-80f4-44ac-a84c-7924c290e1b7%2Fc8b297c8-cf83-415e-8d39-3cd53377d3bc%2F0wlh26l_processed.jpeg&w=3840&q=75)
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